Question
Answer
$$(a-1)(a^2-2a+3)=a^3-3a^2+5a-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a-1)(a^2-2a+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}a^3-2a^2+3a-a^2+2a-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}a^3-3a^2+5a-3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{a-1}\right) $ by each term in $ \left( a^2-2a+3\right) $. $$ \left( \color{blue}{a-1}\right) \cdot \left( a^2-2a+3\right) = a^3-2a^2+3a-a^2+2a-3 $$ |
| ② | Combine like terms: $$ a^3 \color{blue}{-2a^2} + \color{red}{3a} \color{blue}{-a^2} + \color{red}{2a} -3 = a^3 \color{blue}{-3a^2} + \color{red}{5a} -3 $$ |
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